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I'm trying to understand if is possible to say something about the Floquet exponents, in the limit of a very slow changing on time. I try to explain. Given the differential equation

$$

\dot{\vec{v}}(t) = A(t) \vec{v}(t)

$$

with

$$

A(t+T)=A(t)

$$

a monodromy matrix is given by

$$

\Phi(T)

$$

where

$$\Phi(t)$$

is a matrix that is solution of

$$

\dot{\Phi}(t) = A(t) \Phi(t)

$$

and the Floquet exponents can be calculated from the spectrum of this monodromy matrix.

My question is:

can we calculate an expression for the Floquet exponents in terms of the eigenvalues of $$A(t)$$, in the limit $$T\rightarrow \infty$$ ?

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# Adiabatic evolution and floquet theorem

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